Regarding the Tesla Magnifying Transmitter. Does anyone know if there is any math or reasoning regarding the ratio between the diameter of the secondary and extra coils? The Colorado Springs TMT had a ratio of approximately 6 to 1 and this currently appears to be the standard ratio being used. However, I have seen a Eric Dollard's Extra Coil Calculation document in which the extra coil diameter is 40% of the secondary coil. I get the impression that there is some form of magnetic coupling or impedance matching behind the diameter of the coils. If someone could explain the reasoning or post the latest version of Eric's extra coil calculations that would be appreciated.

The Colorado Springs TMT was experimental so there's no particular relationship between the coil dimensions. Through experimentation Tesla found the best combination via adjusting the number of turns and therefore relative impedance of the coils, but there's no "special ingredient" involved. It seems that it was just an experiment to take what he had previously observed when using "extra" coils in series with his flat spiral coil(s) further.

The 6:1 ratio that you're referring to normally refers to the height to diameter ratio of the secondary winding used in standard Tesla coils. Those don't use an extra coil.

Eric's CRI design is slightly different, because the idea there is to experimentally find a hypothetical "magic impedance mismatch" which allows the secondary and extra coil to independently resonate at 1/4 wavelength for twice the voltage gain if you will rather than the total wire length of the secondary + extra coil as one continuous length resonating at 1/4 wavelength. It's not known if that condition is even possible so Eric recommends not to use the extra coil in his design to begin with.

In basic terms, the Colorado Springs extra coil is not meant to be coupled to the primary, it's meant to be as free to resonate as possible in order to get the highest potential gain, so it's connected in series to the top end of the secondary, which is what couples the energy from the primary.

Hi dR-Green, when putting in various custom frequency values for the TMT on the Teslascientific website I notice that the diameter of the secondary coil is about six times the diameter of the extra coil. I assuming that there would be no reason to try extra coils with a larger diameter with respect to the secondary coil, say a secondary to extra diameter ratio of three to one. My reasoning is that while Tesla found the correct ratios during his time at Colorado Springs he was working with very large coils. Smaller setups may have improved results with larger diameter extra coils, but that cannot be verified without experimentation.

I post this to add to what dR-Green says.
there is a mostly boring document that the FBI gave out from a freedom of information act request. Most the good parts are at about 2/3 into reading it. Most the entire first 1/3 is highschool kids asking if the FBI knows about telsa...
one of tesla's lab techs wrote to them with the details of what ball lightning was, how to make, and how to use it as a weapon.
he said that you drive the primary at 1/4 the wavelength of the secondary to get the largest effect.
so, I have to assume that you would then want resonance of each coil to match that if you are looking at the making the ball lightning the will destroy anything near as it decays.
past that, here is an interesting thing that might be research past that point.
it is a PDF download http://blog.lege.net/Mathias_Bage/GL...-annotated.pdf
I started a thread on it on this forum and have been testing it with no results so far,
I mention this because there seems to be an energy requirement to make the unique effects.
not convinced that low power tests get measurable results.